4/x-1+6/3x+1=13/3x+1

Solution for 4/x-1+6/3x+1=13/3x+1 equation:

4/x-1+6/3x+1=13/3x+1

We move all terms to the left:

4/x-1+6/3x+1-(13/3x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We add all the numbers together, and all the variables

4/x+6/3x-(13/3x+1)=0

We get rid of parentheses

4/x+6/3x-13/3x-1=0

We calculate fractions


12x/3x^2+(-13x+6)/3x^2-1=0

We multiply all the terms by the denominator


12x+(-13x+6)-1*3x^2=0

Wy multiply elements

-3x^2+12x+(-13x+6)=0

We get rid of parentheses

-3x^2+12x-13x+6=0

We add all the numbers together, and all the variables

-3x^2-1x+6=0

a = -3; b = -1; c = +6;
Δ = b2-4ac
Δ = -12-4·(-3)·6
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{73}}{2*-3}=\frac{1-\sqrt{73}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*-3}=\frac{1+\sqrt{73}}{-6}
$